Atom-randomization reference state

The mean-force scoring functions based upon an atom-randomized reference state use the method for the simple monatomic system to calculate p (r). In this method, it is assumed that all the atoms are randomly placed in the system without interatomic interactions, ignoring interatomic connectivity, excluded volume, and other factors in the structures of protein-ligand complexes. The resulted pair potentials w,y are then taken as the true potentials Uy despite their differences, and the binding energy score is calculated as... 

Other examples of mean-force scoring functions based on the atom-randomized reference state include MScore [63], ASP [64], KScore [57], etc. 

As discussed in Section 2, the atom-randomized reference state used in calculations for simple fluid systems cannot be generalized to the connected, finite-atomic-size system of protein-ligand complexes. Therefore, researchers attempted to make corrections to the simple random reference state in order to improve the derived mean-force potentials. 

A common reference density, first used by Roux and Daudel (1955), is the superposition of spherical ground-state atoms, centered at the nuclear positions. It is referred to as the promolecule density, or simply the promolecule, as it represents the ensemble of randomly oriented, independent atoms prior to interatomic bonding. It is a hypothetical entity that violates the Pauli exclusion principle. Nevertheless, the promolecule is electrostatically binding if only the electrostatic interactions would exist, the promolecule would be stable (Hirshfeld and Rzotkiewicz 1974). The difference density calculated with the promolecule reference state is commonly called the deformation density, or the standard deformation density. It is the difference between the total density and the density corresponding to the sum of the spherical ground-state atoms located at the positions R... 

Unlike the simple monatomic system in which the p can be exactly obtained by randomizing all the atoms in the system, the reference state p j r) for the complicated protein system is inaccessible due to the effects of connectivity, excluded volume, composition, etc. [45]. Therefore, the pair potentials defined in Eq. (5) are not the exact potentials of mean force in physics. Also, similar to the potential of mean force, the knowledge-based potentials of Eq. (5) are not the true interaction potentials, either. 

The order parameter is essentially a kinematic measure, describing the state of order within a system without any intrinsic reference to what factors drove the system to the state of interest. For example, in thinking about the transition between the ordered and disordered states of an alloy, it is useful to define an order parameter that measures the occupation probabilities on different sublattices. Above the order-disorder temperature, the sublattice occupations are random, while below the critical temperature, there is an enhanced probability of finding a particular species on a particular sublattice. The conventional example of this thinking is that provided by brass which is a mixture of Cu and Zn atoms in equal concentrations on a bcc lattice. The structure can be interpreted as two interpenetrating simple cubic lattices where it is understood that at high temperatures we are as likely to find a Cu atom on one sublattice as the other. A useful choice for the order parameter, which we denote by r], is... 

In a KMC method, it is typically assumed that various possible state-to-state transitions from a given state are well modelled by the Arrenhius law and then molecular dynamics is used to calculate the prefactor A and energy difference AE in order to understand the timescales and relative probabilities of different rare events. A Markov state model can be developed to help understand the global dynamics and simplify the model as a whole. For references on many interesting approaches to this important topic, the reader is referred to [36,42,137,149,391]. Andersen Thermostat. Of particular interest is the simple and useful Andersen thermostat [11]. This method works by selecting atoms at random and randomly perturbing their momenta in a way consistent with prescribed thermodynamic conditions. It has been rigorously proven to sample the canonical distribution [114],... 

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